When the level of confidence and the sample size remain the same,a confidence interval for a population mean µ will be ________________,when the sample standard deviation s is small than when s is large.
A)Wider
B)Narrower
C)Neither A nor B,they will be the same

Question

Quizplus · Accepted Answer

The width of the confidence interval for a population mean µ is determined by the margin of error, which in turn is influenced by the standard error of the mean. The standard error is typically calculated as s/sqrt(n), where s is the sample standard deviation and n is the sample size. Therefore, when the level of confidence and the sample size remain the same, a confidence interval for µ will be narrower when s is smaller because a smaller s will result in a smaller standard error and a smaller margin of error. Thus, the best choice is B.

When the Level of Confidence and the Sample Size Remain